Miscellaneous Problem on Limits 2

Let $f(x) = \ln(x)$ as an example. This gives $\lim_{x \rightarrow \infty} \frac{\ln(3x)}{\ln(x)} = \lim_{x \rightarrow \infty} \frac{\ln(3) + \ln(x)}{\ln(x)} = \lim_{x \rightarrow \infty} \frac{\ln(3)}{\ln(x)} + 1 = 1.$ By the same approach:

$\lim_{x \rightarrow \infty} \frac{\ln(2x)}{\ln(x)} = \lim_{x \rightarrow \infty} \frac{\ln(2)}{\ln(x)} + 1 = \boxed{1}.$